From a technical perspective, this study makes two contributions.
The first is the evaluation of a moment-generating function using variational inequality, following [1]}.
That is, we utilize a dual representation to reform the moment-generating function using an arbitrary distribution and then use the form to derive an upper bound for the deviation of the matrices.
This approach was employed by [2]} and others, and we extend the approach to our setting using random matrices with dependence.
The second is the truncation technique used to ensure that the estimator is robust.
We apply the technique for this problem by truncating eigenvalues of random matrices.
By decomposing the deviation of the empirical mean into deviations from a truncated estimator, we can analyze the effect of the heavy-tail property.
